The present invention relates generally to optical communications and, more particularly, to full-range pilot-assisted frequency offset estimation for orthogonal frequency-division multiplexing OFDM communication systems.
Orthogonal frequency-division multiplexing (OFDM) has attracted much research interest due to its dispersion resistance, ease of frequency domain equalization and high spectral efficiency. However, OFDM systems are very sensitive to carrier frequency offset (FO) and they can only tolerate offsets within a small fraction of the subcarrier spacing. FO will result in loss of orthogonality between subcarriers and thus degrade the system performance. Thus, frequency offset compensation (FOC) is the most critical function to implement. The key challenge in FOC for CO-OFDM systems is to estimate the FO both accurately and efficiently with a full acquisition range.
FIG. 1 shows the maximum frequency offset which an OFDM system can tolerate. Supposing that an OFDM signal covers a bandwidth of Bs, its maximum bandwidth can only go up to the bandwidth of a digital-to-analog converter (DAC) which generates the OFDM signal. Here we use Rs to denote the sampling rate of the DAC. In other words, Rs>=Bs. At the receiver side, after down-converting the OFDM signal into electrical domain, a anti-aliasing low-pass filter is necessary to prevent frequency overlapping when sampling the received signal back to Rs samples per second. The bandwidth of the low-pass filter is also capped at Rs/2 to avoid potential aliasing issue. On the other hand, the local oscillator used in the coherent receiver is very likely to have a different frequency from the transmitter laser which is caused by manufacturing imperfection, overheating, ageing and so on. As a result, the OFDM signal is designed to have guardband to avoid the power loss because of the filtering from anti-aliasing low-pass filter at the receiver side. This guardband will determine the maximum frequency offset which the OFDM signal can tolerate. For example, when the Bs is only half of the total DAC bandwidth and anti-aliasing filter bandwidth is set at its maximum, i.e., Bs=Rs/2 and Be=Rs/2, the frequency offset range of this designed OFDM system can be from −Rs/4 to +Rs/4. Based on this design procedure of the OFDM systems, the proposed pilot-assisted FOE could have this full-range estimation with high accuracy.
The first prior frequency offset compensation FOC method was proposed in 1994 and only achieved an estimation range of half a subcarrier spacing of the training symbol by observing the phase variation between two identical OFDM symbols. Shortened repeated symbols could be used to extend the estimation range, but it would lead to inaccuracy if the symbols are used for channel estimation.
The first group of FOC methods all used multiple shortened identical training symbols (in time domain) to increase the estimation range. A prior effort employed a training symbol composed of L>2 identical parts and thus the estimation range is increased to ±L/2 subcarrier spacing. Other prior efforts also utilize a similar repetitive signal structure inside an OFDM symbol to increase the estimation range. In another prior effort, a fixed-length training-symbol-block, which consists of multiple small identical training symbols, is used. For all the FOC methods based on the repetitive structure, a proper L needs to be tried out and properly picked to cover the correct estimation range and to get accurate result. And additional procedures, like the multistage algorithm adopted in a prior work or extra fine FOC stages in another prior work, are designed to solve the tradeoff between accuracy (smaller L) and range (larger L). Thus, methods based on L repetitive slots within one symbol (or L repetitive shortened symbols) are more usually complicated.
The frequency offset FO can be divided into a fraction and an integer part of the subcarrier spacing. The second group of FOC methods estimates the fraction and integer part of the subcarrier spacing separately. A prior work proposed an efficient FOC algorithm based on the transmission of a training symbol composed of two identical halves in the time domain to get the fraction part of FO. And a second training symbol contains a pseudo noise sequence to estimate the integer part. In a prior work, the author employs a repeated pseudo-noise sequence in the frequency domain. In this kind of approaches, a merit function is usually introduced. The integer part of the FO is estimated by exhaustive search to optimize the merit function over a large number of integer candidates. And the searching space would be as large as the FFT size to obtain the full estimation range. Thus, methods based on maximizing merit function to find the integer part of FO are usually computationally expensive.
These prior FOC methods are designed for wireless systems, where multi-path fading is more troublesome than a large FO. A novel algorithm using sample-shifted training symbols was proposed for the fast acquisition of FO in the CO-OFDM systems. The fractional part is calculated from the cross-correlation function between the two training symbols. The third training symbol is added to estimate the integer part. The temporal samples of the third training symbols are designed to be the same as the first two training symbols, but with a sample shift. And more training symbols of different sample shifts are attached to the training sequence to improve the estimation accuracy. This method is computationally simpler than the previous methods and can cover the full range if p=1, which is unrealistic in practical systems because of signal power filtering by the limited receiver bandwidth. However, it needs at least three training symbols and the parameter of shifted samples needs to be optimized for different value of FO.
Accordingly, there is a need for a frequency offset compensation that improves over the prior art.